Using Ruby to emulate how hardware adds binary numbers

binary_adder.rb

# Sums two bits
def half_adder(a, b)
  sum = a ^ b
  carry = a & b
  [carry, sum]
end

# Sums three bits
def full_adder(a, b, c)
  carry1, sum1 = half_adder(a, b)
  carry2, sum = half_adder(sum1, c)
  carry = carry1 | carry2
  [carry, sum]
end

# Sum two nibbles (a 'nibble' is 4 bits or half a byte)
def sum_nibbles(nibble_a, nibble_b)
  carry0, sum0 = half_adder(nibble_a[3], nibble_b[3])
  carry1, sum1 = full_adder(nibble_a[2], nibble_b[2], carry0)
  carry2, sum2 = full_adder(nibble_a[1], nibble_b[2], carry1)
  carry3, sum3 = full_adder(nibble_a[0], nibble_b[0], carry2)

  [carry3, sum3, sum2, sum1, sum0]
end

def test_half_adder
  [
    [0, 0, 0, 0],
    [0, 1, 0, 1],
    [1, 0, 0, 1],
    [1, 1, 1, 0]
  ].each do |fixture|
    a, b, *expected = fixture
    result = half_adder(a, b)
    raise [fixture, result].to_s unless result == expected
  end

  'pass'
end

def test_full_adder
  [
    [0, 0, 0, 0, 0],
    [0, 0, 1, 0, 1],
    [0, 1, 0, 0, 1],
    [1, 0, 0, 0, 1],
    [0, 1, 1, 1, 0],
    [1, 0, 1, 1, 0],
    [1, 1, 0, 1, 0],
    [1, 1, 1, 1, 1]
  ].each do |fixture|
    a, b, c, *expected = fixture
    result = full_adder(a, b, c)
    raise fixture.to_s unless result == expected
  end

  'pass'
end

def test_sum_nibbles
  [
    { a: [0, 0, 0, 1], b: [0, 0, 0, 0], sum: [0, 0, 0, 0, 1] },
    { a: [0, 0, 0, 1], b: [0, 0, 0, 1], sum: [0, 0, 0, 1, 0] },
    { a: [0, 0, 0, 0], b: [1, 1, 1, 1], sum: [0, 1, 1, 1, 1] },
    { a: [1, 1, 1, 1], b: [1, 1, 1, 1], sum: [1, 1, 1, 1, 0] }
  ].each do |fixture|
    result = sum_nibbles(fixture[:a], fixture[:b])
    raise [fixture, result].to_s unless result == fixture[:sum]
  end

  'pass'
end

[
  :test_half_adder,
  :test_full_adder,
  :test_sum_nibbles
].each { |t| puts '%s: %s' % [t, send(t)] }